A Functional Inequality in Restricted Domains of Banach Modules

Abstract

<p/> <p>We investigate the stability problem for the following functional inequality <inline-formula><graphic file="1687-1847-2009-973709-i1.gif"/></inline-formula> on restricted domains of Banach modules over a <inline-formula><graphic file="1687-1847-2009-973709-i2.gif"/></inline-formula>-algebra. As an application we study the asymptotic behavior of a generalized additive mapping.</p